## Cornelia Busch: Catalogue data in Autumn Semester 2019 |

Name | Dr. Cornelia Busch |

Address | Lehre Mathematik ETH Zürich, HG G 34.2 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 82 69 |

cornelia.busch@math.ethz.ch | |

Department | Mathematics |

Relationship | Lecturer |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-0203-00L | Mathematics | 4 credits | 3V + 1U | C. Busch | |

Abstract | This course gives an introduction to the following subjects: linear algebra (systems of linear equations, matrices, eigenvectors), calculus, multivariable calculus, differential equations. | ||||

Objective | Basic mathematical knowledge for engineers. Mathematics as a tool to solve engineering problems. | ||||

Content | This course gives an introduction to the following subjects: linear algebra (systems of linear equations, matrices, eigenvectors), calculus, multivariable calculus, differential equations. | ||||

Literature | Tom M. Apostol, Calculus, Volume 1, One-Variable Calculus with an Introduction to Linear Algebra, 2nd Edition, Wiley Tom M. Apostol, Multi-Variable Calculus and Linear Algebra with Applications, 2nd Edition, Wiley Ulrich L. Rohde, Introduction to differential calculus : Systematic studies with engineering applications for beginners, Wiley. Ulrich L. Rohde, Introduction to integral calculus : Systematic studies with engineering applications for beginners, Wiley. Serge Lang, Introduction to Linear Algebra, 2nd edition, Springer New York. Serge Lang, A First Course in Calculus, 5th edition, Springer New York. A list will be handed out in the lecture. | ||||

401-0373-00L | Mathematics III: Partial Differential Equations | 4 credits | 2V + 1U | T. Ilmanen, C. Busch | |

Abstract | Examples of partial differential equations. Linear partial differential equations. Separation of variables. Fourier series, Fourier transform, Laplace transform. Applications to solving commonly encountered linear partial differential equations (Laplace's Equation, Heat Equation, Wave Equation). | ||||

Objective | Classical tools to solve the most common linear partial differential equations. | ||||

Content | 1) Examples of partial differential equations - Classification of PDEs - Superposition principle 2) One-dimensional wave equation - D'Alembert's formula - Duhamel's principle 3) Fourier series - Representation of piecewise continuous functions via Fourier series - Examples and applications 4) Separation of variables - Solution of wave and heat equation - Homogeneous and inhomogeneous boundary conditions - Dirichlet and Neumann boundary conditions 5) Laplace equation - Solution of Laplace's equation on the rectangle, disk and annulus - Poisson formula - Mean value theorem and maximum principle 6) Fourier transform - Derivation and definition - Inverse Fourier transformation and inversion formula - Interpretation and properties of the Fourier transform - Solution of the heat equation 7) Laplace transform (if time allows) - Definition, motivation and properties - Inverse Laplace transform of rational functions - Application to ordinary differential equations | ||||

Lecture notes | See the course web site (linked under Lernmaterialien) | ||||

Literature | 1) S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY. 2) N. Hungerbühler, Einführung in partielle Differentialgleichungen für Ingenieure, Chemiker und Naturwissenschaftler, vdf Hochschulverlag, 1997. Additional books: 3) T. Westermann: Partielle Differentialgleichungen, Mathematik für Ingenieure mit Maple, Band 2, Springer-Lehrbuch, 1997 (chapters XIII,XIV,XV,XII) 4) E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons (chapters 1,2,11,12,6) For additional sources, see the course web site (linked under Lernmaterialien) | ||||

Prerequisites / Notice | Required background: 1) Multivariate functions: partial derivatives, differentiability, Jacobian matrix, Jacobian determinant 2) Multiple integrals: Riemann integrals in two or three variables, change of variables 2) Sequences and series of numbers and of functions 3) Basic knowledge of ordinary differential equations |